Question

The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each.
Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game:
1.At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each.
2.At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points.
3.Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round.
4.In exactly two out of the six rounds, Arun was the only player who bid Hi.
In how many rounds did Dipak gain exactly 1 point? [This Question was asked as TITA]

• A. 1 round
• B. 3 rounds
• C. 2 rounds
• D. 5 rounds

Answer 1

The Correct Option is A

To solve the problem, we need to analyze the information given and track the score changes across rounds based on the rules of the Hi-Lo game and the statements provided. Let us follow these steps:

• Understand Score Changes: Based on the game rules, we have:
  • If all four bid Hi, all lose 1 point each.
  • If three bid Hi, one bids Lo, the three gain 1 point each, and the one loses 3 points.
  • If two bid Hi, two bid Lo, the two Hi gain 2 points each, and the two Lo lose 2 points each.
  • If one bids Hi, three bid Lo, the one Hi gains 3 points, and the three Lo lose 1 point each.
  • If all bid Lo, all gain 1 point each.
• Initial Scores: At the end of round 3: Arun: 6, Dipak: 2, Bankim: -2, Charu: -2.
• Final Scores: At the end of round 6: Arun: 7, Dipak: -1, Bankim: -1, Charu: -5.
• Score Changes (Round 4 to Round 6):
  
  • Arun from 6 to 7 (+1): Must have all Lo bids once as Arun gains 1 point.
  • Bankim from -2 to -1 (+1): Gains 1 point.
  • Dipak from 2 to -1 (-3): Dipak loses 3 points in non-Lo rounds.
  • Charu from -2 to -5 (-3): Consistently loses points.
• Dipak's Score Analysis:
  1. From Score 2 to -1 over rounds 4 to 6, Dipak loses 3 points in total.
  2. In one of these rounds, Dipak would have scored +1 from the configuration of Hi-Lo bids.
• Verification by Facts:
  1. Fact 3: Dipak's score in round 3 (2 points) is between his scores in rounds 1 and 2.
  2. Based on scoring possibilities, Dipak must have gained +1 exactly once to fit between the given boundaries and other rounds contributing to decrease.
  3. Fact 4: Arun was the sole Hi-bidder in exactly two rounds, aligning rounds 3 and 6 with this scenario as possible candidates.

Thus, based on the analysis and given conditions, Dipak gains exactly 1 point in 1 round. This confirms the answer.